Value Indefiniteness, Randomness and Unpredictability in Quantum Foundations
type: CreativeWork
description: The outcomes of quantum measurements are generally considered to be random, but despite the fact that this randomness is an important element in quantum information theory, its nature is not well understood. In this thesis, we study several issues relating to the origin and certification of quantum randomness and unpredictability. One of the key results in forming our understanding of quantum mechanics as an intrinsically indeterministic theory is the Kochen-Specker theorem, which shows the impossibility to consistently assign simultaneous noncontextual definite values to all quantum mechanical observables prior to measurement. However, the theorem, under the assumption that any definite values must be noncontextual, only strictly shows that some observables must be value indefinite. We strengthen this result, proving a stronger variant of the Kochen-Specker theorem showing that, under the same assumption, if a system is prepared in an arbitrary state j i, then every observable A is value indefinite unless j i is an eigenstate of A. The indeterministic nature of quantum measurements does little to explain how the quality of quantum randomness differs from classical randomness. We show that, subject to certain physical assumptions, a sequence of bits generated by the measurement of value indefinite observables is guaranteed, in the infinite limit, to be strongly incomputable. We further discuss how this can be used to build a quantum random number generator certified by value indefiniteness. Next, we study the notion of unpredictability, which is central to the concept of (quantum) randomness. In doing so, we propose a formal model of prediction that can be used to asses the predictability of arbitrary physical experiments. We investigate how the quantum features of value indefiniteness and complementarity can be used to certify different levels of unpredictability, and show that the outcome of a single measurement of a value indefinite quantum observable is formally…
abstract: The outcomes of quantum measurements are generally considered to be random, but despite the fact that this randomness is an important element in quantum information theory, its nature is not well understood. In this thesis, we study several issues relating to the origin and certification of quantum randomness and unpredictability. One of the key results in forming our understanding of quantum mechanics as an intrinsically indeterministic theory is the Kochen-Specker theorem, which shows the impossibility to consistently assign simultaneous noncontextual definite values to all quantum mechanical observables prior to measurement. However, the theorem, under the assumption that any definite values must be noncontextual, only strictly shows that some observables must be value indefinite. We strengthen this result, proving a stronger variant of the Kochen-Specker theorem showing that, under the same assumption, if a system is prepared in an arbitrary state j i, then every observable A is value indefinite unless j i is an eigenstate of A. The indeterministic nature of quantum measurements does little to explain how the quality of quantum randomness differs from classical randomness. We show that, subject to certain physical assumptions, a sequence of bits generated by the measurement of value indefinite observables is guaranteed, in the infinite limit, to be strongly incomputable. We further discuss how this can be used to build a quantum random number generator certified by value indefiniteness. Next, we study the notion of unpredictability, which is central to the concept of (quantum) randomness. In doing so, we propose a formal model of prediction that can be used to asses the predictability of arbitrary physical experiments. We investigate how the quantum features of value indefiniteness and complementarity can be used to certify different levels of unpredictability, and show that the outcome of a single measurement of a value indefinite quantum observable is formally…
author: Abbott, Alastair
license: https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
date published: 2015
date modified: 2026-07-24T01:03:56Z
provider: University of Auckland
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: ResearchSpace@Auckland

PropertyValue
property ID: Handle
value: https://hdl.handle.net/2292/27774